System and method for battery charging

ABSTRACT

A method for charging a lead acid storage battery to advantageously extend its life is described. The termination of a charging process is based upon an evaluation of the first derivative (dv/dt) and second derivative (d2v/dt2) of the applied charging voltage. By utilizing the first derivative (dv/dt) and second derivative (d2v/dt2) as charging criteria, an amount of overcharge is applied to the battery that takes into account the precise amount of amp-hours previously removed from the battery. A charger arrangement for performing a charging process of the invention also is described.

CROSS-REFERENCE TO RELATED APPLICATION

This application is the National Stage of International Application No.PCT/US01/31141 filed 3 Oct. 2001 and claims the benefit thereof.

FIELD OF THE INVENTION

This invention pertains to a method for controlling the termination of arecharging process for flooded deep-cycle lead acid electric storagebatteries. More particularly, it pertains to procedures which supply tosuch batteries a quantity of recharge energy which is directly relatedto the amount of energy discharged following the last preceding batterycharge event. It also pertains to equipment for implementing suchprocedures.

BACKGROUND OF THE INVENTION

Rechargeable electric storage batteries of many different kinds areknown, such as nickel-cadmium, nickel metal hydride, nickel-iron,lithium, silver-cadmium and deep-cycle lead acid batteries. Deep-cyclelead acid batteries differ from SLI (starting, lighting, ignition) leadacid batteries used, e.g., in conventional automobiles; SLI batteriesare not designed or constructed to withstand repeated cycles ofsubstantial discharge and recharge, and so are not rechargeablebatteries in the sense of this invention.

It is known, such as from U.S. Pat. Nos. 4,392,101 and 4,503,378, thatthere are certain characteristics of a rechargeable battery, regardlessof kind, which change during recharging of the battery in ways whichsignal either that the battery is fully charged or that it is at arelatively predictable point short of but near a state of full charge.Those patents, as well as other publications, describe equipment andtechniques for monitoring those characteristics and for detectingcertain events, conditions or states of them, and using such detectionseither to terminate the battery charging process or to continue chargingfor preset times or in preset ways. Those preset ways typically usecharging processes different from those in use at the time of thedetected event. Those charging event detection techniques are known asinflection analysis methods because they rely on the detection ofcertain inflection points in time-based curves which describe the changein battery voltage or battery current, e.g., during the chargingprocess. While inflection analysis as described to date works well tocontrol recharging of most kinds of rechargeable batteries, inflectionanalysis as heretofore described has been found not to servesatisfactorily for controlling recharging of flooded deep-cycle leadacid batteries in which the battery electrolyte is a liquid (typicallysulfuric acid) unconfined in any supporting matrix such as a gel.

Flooded deep-cycle lead acid batteries are widely used as energy sourcesfor electrically powered vehicles such as golf cars, fork lift trucks,and scissor lift vehicles. They also are used in uninterruptible powersupplies in hospitals and other buildings and facilities, and ascomponents of photovoltaic power installations. The reasons whyinflection analysis techniques as heretofore described are notsatisfactory for controlling recharging of flooded deep-cycle lead acidbatteries can be understood from the use of such batteries in electricgolf cars, as an example.

Electric golf cars are powered by sets of 4, 6 or so flooded deep-cyclelead acid electric batteries. At a given golf course, there is a fleetof such golf cars available for use by golfers. Different cars in thefleet may have older batteries in them than other cars in the fleet.Certain cars may be used more frequently than others. Some cars may beused longer on a given day than others. Some cars may be subjected tomore strenuous usage conditions on a given day than others, depending onthe circumstances of the using golfers or differences in traversedterrain, among other reasons. Also, it is well known that even if allbatteries in the fleet are from the same manufacturer and are of thesame nominal age, there still will be meaningful variations betweenbatteries of kinds which can affect battery performance, life and,importantly, how they respond to recharging processes. As a consequence,at the end of a day when the golf cars in that fleet are to berecharged, there can be significant differences between the dischargestates of the batteries from car to car, and consequent meaningfuldifferences from car to car in how the batteries need to be charged.Fleet-wide uniform recharging procedures either will cause somebatteries to be insufficiently recharged or, more likely, substantialnumbers of the batteries will be materially overcharged. Materialovercharge of such a battery reduces battery life. Very commonly, thepersons employed to recharge fleets of golf cars have no understandingof the effects of substantial overcharge and how to determine when it isoccurring. Therefore, it is desirable that the batteries used inelectric golf cars be recharged by equipment and processes which avoidsubstantial overcharge and do so in ways which inherently accommodateand deal with differences between batteries due to discharge state, age,and manufacturing variations, among other factors.

Deep-cycle lead acid batteries are designed to withstand repeated cyclesof substantial discharge from a fully charged state and of recharge froma discharged state to a state of full charge. As compared to other kindsof rechargeable batteries which do not use liquid electrolytes, theliquid acid electrolyte of flooded deep-cycle lead acid batteriespresents special conditions which require that a given battery, or agiven set of a small number of batteries repeatedly used in combinationwith each other, be recharged in a way which provides a controlledovercharge related in extent to the state of the battery at the time arecharge event is commenced. Stated differently, effective recharge of aflooded deep-cycle lead acid battery ideally should include a controlledovercharge determined by the amount of energy removed from (dischargedby) the battery during its last preceding duty cycle (period of usefollowing the last prior charging event). The reason is related to whathappens to the liquid electrolyte during the prior duty cycle and thefollowing recharge event.

As a cell of a lead acid battery discharges, the acid ions in theelectrolyte move to the cell electrodes and oxygen atoms move from theactive material of the cell into the electrolyte to form water with theelectrolyte hydrogen ions. As a consequence, the electrolyte acidbecomes progressively more diluted and its specific gravityprogressively approaches 1.0 from a higher starting specific gravity. Asthe cell is recharged, that ion exchange process is reversed to produceregeneration of the electrolyte acid and the active material. If theelectrolyte is present in the cell as a free liquid (i.e., the cell isflooded), as opposed to being present in a gel matrix, the regeneratedacid, being heavier than the dilute electrolyte, sinks to the bottom ofthe cell as it is created. As the recharging process continues, more andmore concentrated regenerated acid collects in the bottom of the cell.At the point at which the cell active material has been fullyregenerated, the cell is theoretically fully recharged on a Coulombicbasis. However, the cell is not in good condition for use to deliverstored electrical energy because of the stratification of theelectrolyte. The electrolyte is not of uniform acidity throughout thecell and so the regenerated acid electrolyte is not in uniformlyeffective contact with the regenerated active material over the fullarea of the regenerated active material; if the cell were to be calledupon to discharge at that point, the discharging electrochemical processwill occur predominantly in the lower part of the cell where theelectrolyte acid is overly concentrated. The cell will not dischargeenergy at the levels desired, and the over concentrated acid in thebottom of the cell will cause overly rapid degradation of the adjacentactive material. The consequence is under performance of the cell in amanner which materially reduces cell life.

In the portion of the recharge process for a lead acid battery cellwhich immediately precedes full regenerative restoration of the activematerial, gas is generated in the cell as a normal part of the rechargeprocess. The gas bubbles rise through the electrolyte to the top of thecell and, in the process, induce circulation (stirring) of theelectrolyte in the cell. However, if the recharge process is terminatedat the point of full regeneration of the active material, the amount ofgas generation which will have occurred will be insufficient to stir theelectrolyte adequately to cause it to be of uniform acid concentration(uniform specific gravity) throughout the cell. For that reason, it iscommon practice to continue the process of recharging a floodeddeep-cycle lead acid battery beyond the point of full recharge, i.e., toextend the gas generation process for a time to achieve adequatestirring of the regenerated electrolyte. That is, the cell isintentionally overcharged.

Current practice is to overcharge such batteries, which include a numberof cells, by a predetermined amount which is defined to be adequate tofully stir the electrolyte in the cell or cells which need the moststirring; that definition of the predetermined amount of overcharge isbased on the assumption that the cell has been maximally discharged inits previous duty cycle and that the cell has certain properties of age,condition and temperature. However, as shown above in the discussion ofthe operation of a fleet of electric golf cars, that assumption is notapt for a substantial portion of batteries requiring recharge. As aresult, reliance upon that assumption about the amount of overcharge tobe applied in the terminal stages of recharging flooded deep-cycle leadacid storage batteries causes a substantial number, if not the majority,of such batteries to be meaningfully overcharged. Meaningful overchargeof such a battery, especially if repeated more than a few times,substantially reduces the effective life of such a battery.

The foregoing description provides a foundation for understanding howexisting descriptions of inflection analysis techniques for controllingbattery recharge processes are deficient when applied to the rechargingof flooded deep-cycle lead acid storage batteries.

U.S. Pat. No. 4,392,101 is an early description of the use of inflectionanalysis in controlling recharging of rechargeable batteries. It teachesthat rechargeable batteries in general have broadly similar responsecharacteristics to recharging processes. It teaches that if batteryvoltage or current, e.g., is plotted graphically against time duringrecharge, the resulting voltage/time or current/time curves will havebroad similarities. After initiation of the charge process, irrespectiveof the particular materials used to define a battery cell, those curveswill manifest at least a pair of inflection points in which the graphline reverses curvature, i.e., is inflected. It is disclosed that thoseinflection points signal or denote different phases of the battery'sresponse to applied charging energy and, for each type of cell, thoseinflections occur at relatively predictable times in the process, eitherbefore or at the time of the battery reaching a state of full charge. Itis disclosed that the predictability of the inflection point occurrencesis generally unaffected by (happens without regard to) factors such asthe actual voltage of the battery, individual cell characteristics,individual charging history, or actual ambient temperature conditions.That patent discloses that the inflection points can be identified byobserving the state or character of the first or second derivative withrespect to time of the battery characteristic (voltage or current) beingmonitored. More particularly, it teaches that a graph of the secondderivative will cross the zero axis (the sign of the derivative willchange from positive to negative, or vice versa) at least twice duringthe charging process, and the second zero axis crossing of thatderivative either will occur at the time the battery reaches fill chargeor will occur at some interval shortly before fill charge is achieved.However, in the instance of lead acid batteries, that patent does notattempt to describe when the second time-based derivative of voltageoccurs relative to full charge. The principal descriptions of thatpatent are in the context of nickel-cadmium batteries where rechargingis terminated a preset time after that second zero-axis crossing of thatderivative has been detected. Nickel-cadmium batteries do not use avariable density electrolyte which is present as a part of the chemicalprocess and so such batteries do not benefit from or require any measureof overcharge.

U.S. Pat. No. 4,503,378 applies inflection analysis recharging controlsto nickel-zinc batteries and discloses that, for that type of battery,recharging is to be terminated upon the occurrence of the secondinstance of sign change (zero axis crossing) of the second derivative ofbattery voltage with respect to time. It also observes that, at the sametime as the second derivative crosses the zero axis from positive tonegative, the value of the first derivative of battery voltage withrespect to time is at a maximum or peak value, a fact which enables thesecond derivative's zero crossing to be confirmed.

The article titled “Charge batteries safely in 15 minutes by detectingvoltage inflection points” appeared in the Sep. 1, 1994, issue of EDNMagazine. That article focuses principally upon fast recharging ofnickel-cadmium batteries. It comments that inflection analysis alsoapplies to lead acid batteries. In that connection, it states “Inlead-acid batteries, the second dV/dt inflection occurs at a predictableinterval before the batteries reach full charge, but from the battery'sAhr capacity rating, you can easily derive the duration of theincremental charging needed to achieve full charge.” That statement doesnot contribute, for at least two reasons, to a solution to the problemof how to efficiently, reliably and effectively charge a floodeddeep-cycle lead acid battery, without meaningfully overcharging it, interms of the battery's true need for recharge. First, a lead acidbattery's Ahr (ampere-hour) capacity rating is not a precise value whichcan be determined accurately from engineering information. Rather, it isa value which a battery manufacturer assigns to a model or type ofbattery as a result of business factors peculiar to the manufacturer,such as marketing objectives, warranty policies, and other factors. Abattery's ampere-hour capacity rating is merely a manufacturer'sstatement of the expectable performance, perhaps under unspecifiedconditions, of an average battery of that kind or type. It has noreliable relation to the charging needs of a particular battery aftercompletion of a particular duty cycle, i.e., its depth of dischargebefore experiencing a recharging event. Second, the ampere-hour capacityrating is a value which needs to be known from a source other than thebattery itself. What is needed is a way to charge a flooded deep-cyclelead acid battery using information, derived from the battery itself,which describes the battery's discharge state and which is usable toovercharge the battery only enough to stir the regenerated electrolyteadequately.

Neither of the patents cited above nor the EDN Magazine article considerthe state of battery discharge before a recharging process is commenced.They impart no knowledge about how information about that dischargestate can be used to control recharge of that battery. However, apartfrom those descriptions it is known (such as from U.S. Pat. No.6,087,805) to physically attach to a battery, such as a battery in agolf car, an integrating ampere meter (ampere hour meter) which travelswith the battery at all times. When the battery is connected to acharger following the battery duty cycle, the “on board” ampere hourmeter is connected to the charger so it can communicate to the chargerthe value of ampere hours removed from the battery during that last dutycycle. That information is applied in the charger to a computing andcontrol device which computes the total charge to be delivered to thebattery by multiplying the metered value of ampere hours by the desiredfactor (for example 1.10 or 110%)that has been found to producesufficient stirring in the electrolyte. A computing and control devicein the charger then monitors the ampere hours returned to the battery bythe charger. When the calculated value for the charge return is reached,that computing and control device instructs the charger to terminate thecharging process. While this approach is effective, it suffers from theadded complexity of communicating data to the charger from the amperehour meter which is associated with the battery. That approach alsosuffers from the added expense of equipping every battery, or everyoperational set of batteries, with its own captive ampere hour meterwhich must be specially constructed to survive in the environment of thebattery. That approach is independent of inflection analysis and hasapparent practical problems in the field.

It is apparent, therefore, that a need exists for the availability ofequipment and procedures which can be used effectively, efficiently andreliably by persons having little or no knowledge of battery technologyto adequately recharge flooded deep-cycle lead acid batteries withoutmeaningfully overcharging any one or small group of batteries. Suchequipment and procedures, to satisfy that need, should effectivelyaddress and conform to the actual recharge and electrolyte stirringneeds of a battery or of a defined small group of batteries. The term“defined small group” means a number of batteries, such as thoseinstalled in a given electric golf car, which most probably will be ofthe same age, will have experienced the same usage history, and willhave shared the same duty cycle in the interval between last beingrecharged as a group and the recharge event of interest.

SUMMARY OF THE INVENTION

In light of the foregoing, this invention addresses problem situationsnot heretofore resolved in the art to provide procedures and equipmentby which flooded deep-cycle lead acid batteries, individually or indefined small groups, are rechargeable in terms of actual rechargerequirements and minimal overcharge processes. The invention appliesinflection analysis principles in new ways to customize each batterycharging event to the needs of the battery, or battery set, presented tothe charger which includes a novel computing and control device. Thesebenefits and advantages are provided and achieved effectively andreliably without calling for any change in how the battery is made orused. Service personnel are required only to connect and to disconnectthe charger to and from the battery.

Information about recharge requirements is obtained by the charger fromthe battery itself in the course of the charging process, withoutreliance upon an ampere hour meter matched to the battery. That is, thecharger does not know, and does not need to know, the discharge state ofthe battery before the recharging process is commenced. The invention ismaximally protective of the batteries themselves and can lead toextended battery life.

In terms of procedure, the invention provides a method for charging leadacid batteries. The method includes monitoring the battery voltageduring the performance of the process, recording the charging time, andmonitoring the charge provided to the battery in ampere hours. Themethod also includes determining a point in the charging process atwhich the battery has a charge state having a known relation to a fullcharge state, and determining the quantity of charging energydeliverable to the battery beyond a point of full charge which is equalto a desired portion of the energy deliverable between commencement ofthe process and the point at which the battery is fully charged.

In terms of its structural aspects, the invention provides a charger forcharging lead acid batteries, preferably deep cycle lead acid batteries.The charger includes a DC current source, a voltmeter, an ammeter, atimer, a dv/dt measurement circuit, and a d²v/dt² measurement circuit.

More specifically, the charger also includes a controller coupled to theDC current source, the ammeter, the voltmeter, the timer and the dv/dtand d²v/dt² measurement circuits. The controller is configured todetermine the time in a battery recharge event when a battery is atsubstantially a predetermined percentage of full charge and to determinethe value of Q_(D) from the relation (Q_(S)/p)=[Q_(D)/(1+x)] in whichQ_(S) is the ampere-hours of charging energy delivered to the battery inthe interval from the beginning of the event to the time at whichd²v/dt²=0 and dv/dt is maximum, p is the decimal equivalent of thepercentage of replenishment charge delivered to the battery whend2_(v)/dt²=0, x is the decimal equivalent of a desired percentage amountof replenishment charge to be delivered to the battery as an overchargeamount, and Q_(D) is the ampere hours to be delivered to the batteryfrom the beginning of the event to reach the overcharge amount. If thepredetermined percentage of full charge is 98%, then p=0.98.

DESCRIPTION OF THE DRAWINGS

These and other features and advantages of the present invention will bebetter understood from the following detailed description read in lightof the accompanying drawings, wherein:

FIG. 1A is a graph of aspects of voltage and current at the terminals ofa lead acid storage battery being charged with a conventionalferroresonant charger, graphed over time during a typical chargingcycle;

FIGS. 1B and 1C are graphs for the charging profile of similar batteriesat 80 degrees Fahrenheit and 122 degrees Fahrenheit respectivelyfollowing a duty cycle discharge of about 135 ampere-hours;

FIGS. 1D and 1E are graphs for the charging profile of similar batteriesat 80 degrees Fahrenheit and 48 degrees Fahrenheit respectivelyfollowing a duty cycle discharge of about 81 ampere hours;

FIG. 2 is a flow diagram of an embodiment of a charging process for aflooded deep cycle lead acid storage battery;

FIGS. 3A and 3B are flow diagrams of an embodiment of a charging processthat monitors cell voltage;

FIGS. 4A and 4B are a flow diagram of an embodiment of a chargingprocess that monitors cell voltage and charging time;

FIG. 5 is a flow diagram of an embodiment of a charging process thatprovides refresh charging;

FIG. 6 is a flow diagram of an embodiment of a charging process thatmonitors time since the termination of charging and battery open circuitvoltage;

FIG. 7 is a flow diagram of an embodiment of the invention that allowsselection of different charging profiles;

FIG. 8 is a system block diagram of an embodiment of a battery chargingsystem utilizing a charge process control device IC and a measuringcomputing and control device (“MCCD”); and

FIG. 9 is a block diagram of an embodiment of a battery chargerutilizing an embodiment of the invention's process to charge a battery.

GLOSSARY

-   Full charge Q_(F): the state of a battery at which it is at full    charge capacity and continued application of charging energy has no    beneficial effect upon the electrodes or upon electrode active    materials;-   Initial state of charge Q_(i): the amount of residual charge    possessed by a battery at the commencement of a battery recharge    event or process;-   Replenishment charge Q_(R): the amount of charging energy, measured    in ampere-hours, absorbed by the battery having an initial state of    charge to return the battery to a state of full charge;    Q_(R)=Q_(F)−Q_(i)-   Charge deficiency: the difference between a battery's fill charge    and initial state of charge; it is equal to the replenishment charge    Q_(R)-   Overcharge Q_(o): the amount of charging energy, measured in ampere    hours, delivered to a battery in the course of a recharge event or    process after the time the battery achieves full charge until the    termination of the event or process; it is extra energy delivered to    the battery to condition the battery for good performance during its    next duty cycle; in the practice of this invention, its magnitude is    directly related to the magnitude of the replenishment charge;-   Duty cycle: the period after a battery has been fully recharged    during which the battery delivers energy during use of the thing in    which the battery is located or to which it is connected; the    battery charge at the end of a duty cycle is the battery's initial    state of charge in the following battery recharge event or process;-   Coulombic charge Q_(C): the amount of charge possessed by a battery    at any time of interest;-   Delivered charge Q_(D): the ampere hours of energy delivered to a    battery during the interval between commencement and termination of    a battery recharge event or process; in the practice of this    invention it is the combination of the replenishment and overcharge    ampere hours, i.e., Q_(D)=Q_(R)+Q_(O);-   Signal charge Q_(S): the amount of charge, measured in ampere hours,    delivered to a battery during the interval beginning with the    commencement of the recharging process and ending at that later    point in the process at which the battery, due to its particular    electrochemistry, has a detectable condition indicative that the    battery charge level has a definite relation to full charge; in the    context of this invention which pertains to lead acid battery    electrochemistry, the detectable condition is a zero value of the    second time-based derivative of battery voltage coexisting with a    maximum value of the first time-based derivative of battery voltage.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1A is a graph of aspects of the voltage and the current at theterminals of a lead acid storage battery being charged with aconventional ferroresonant charger graphed over time during a typicalcharging cycle; the graphed aspects are voltage, current, and the firstand second derivatives of the voltage with respect to time. Such acharging characteristic is typically observed when charging a lead acidbattery with a ferroresonant battery charger. A ferroresonant chargertypically includes a transformer and rectifier circuit that contributesto the distinctive shapes of the curves describing the way the current128 and voltage 101 vary during a battery charging event. Inimplementing a charging cycle the duration of the charging cycle and therate at which recharging energy is applied to the battery determines theamount of charge returned to the battery. To fully charge a flooded leadacid battery, a typical method utilized is to continue to charge, i.e.,to overcharge, the battery after it has reached a state where chargingcurrent flowing into the battery has decreased significantly.

Controlling overcharge of a lead acid storage battery to a fixedpercentage of ampere hours removed from the battery during animmediately previous duty cycle typically tends to greatly increase abattery's lifetime. Overcharge parameters are typically selected basedupon varying criteria known to those skilled in the art. A battery thuscharged to a fixed percentage of ampere hours removed in the prior dutycycle typically may have a longer useful life than a comparable batterywhich receives, each time it is recharged, an amount of overchargedefined as a fixed percentage of the total charge capacity of thebattery. Thus, knowledge and use of the initial battery discharge statewhen recharging begins aids in determination of the amount of overchargebest delivered to the battery.

A voltage response 101 during charging of a lead acid storage battery isshown as a function of time in FIG. 1A. The voltage measured is thatpresent across the battery's terminals at various times during thecharging cycle. A particular voltage response 101 for each chargingcycle of a battery, in response to a given value of an impressedcharging current 128, changes as a function of the battery's temperatureand internal conditions, which normally are a function of a battery'sage. Neither the temperature nor the age of a battery are known byatypical charging device. Thus, the basis for judging the chargedeficiency of a battery connected to a charger may not be reliably basedon an absolute value of voltage.

A determination of the ampere hours of battery charge deficiency is morereliably based upon inherent voltage-time characteristics of floodedlead acid storage batteries. The inherent voltage-time characteristicspreferably utilized (see FIG. 1A) are voltage as a function of time V(t)(curve 101), the rate of change of voltage over time dv/dt (curve 104),and the acceleration of the voltage over time d²v/dt² (curve 106).

A battery's voltage V(t), as measured across its external terminals,varies during a charging cycle in response to an impressed chargingcurrent I(t) (curve 128 in FIG. 1A). A voltage across the terminals of abattery being charged and a charging current into the battery arerelated by a battery's internal resistance and back EMF (open circuitvoltage) that typically varies during a charging cycle.

At a given time, a battery's internal resistance is determined by aseries of conductive elements that make up a battery's cell structuredisposed in the battery's electrolyte. At initiation of a chargingcycle, or t=0 (see point 116 in FIG. 1A), the initial battery voltageV_(i) is the open circuit voltage. At initiation of the charging cycle,the current supplied by a charger typically is at its highest valueI_(i) (point 126) during a charging cycle.

During a typical charging process, battery voltage 101 is initially at alow value V_(i), rises rapidly to an intermediate voltage from which thevoltage continues to rise slowly for a period of time, after which thevoltage rises rapidly again with an increasing slope where it finallylevels to a final fully charged voltage V_(t). As the battery ischarged, the battery back EMF rises due to heat generated in thecharging process and due to rising specific gravity of the electrolyte.As the battery charges, current 128 supplied by a charger decreases asthe battery voltage 101 increases in step with the increasing batteryimpedance.

In the final stages of charging, a further increase in battery back EMFis caused by the electrolytic generation of hydrogen and oxygen gas asthe electrolyte decomposes in response to the applied energy; thatphenomenon is called “out gassing”. Out gassing occurs as the batterynears and reaches a state of full charge, and its components can nolonger accept recharging energy in a regenerative way. As the outgassing process stabilizes, the voltage across the battery's terminalsremains essentially constant and approaches its final value.

In the final stages of charging, a slight increase in battery terminalvoltage 101 appears due to an electrolyte stirring effect. Theelectrolyte stirring effect is caused by the out gassing process. Thestirring effect causes the electrolyte within each of a series of cellsin the battery to become substantially homogeneous, i.e., of uniformspecific gravity (acid concentration), stabilizing the battery back EMFwithin each cell. It is often desirable to design a battery chargingsystem that takes a battery's internal construction, and the chargingprocess into consideration in order to provide a desirable chargingprocess.

Battery chargers are constructed utilizing various types of circuitdesigns. Circuit designs of chargers include ferromagnetic and switchingtechniques. The various types of battery chargers are also designed toprovide one or more charging processes called “profiles” or “algorithms”that are compatible with the circuit design of the charger. Profiles arealso often selected to take advantage of the internal changes in thebattery during charging in an attempt to extend battery life.

A charger which has a termination scheme keyed to dv/dt=0 typicallyprovides 118% to 124% of the charge previously taken out of the battery.

Continuing with reference to FIG. 1A, the first derivative 104 and thesecond derivative 106 of voltage with respect to time provide additionalinformation concerning a battery's desired charging requirements. Inaddition, the first and second voltage derivatives provide distincttransitions of state that are easily detected. The information providedby those first and second derivatives provides reliable criteria thatare unique to an individual battery, so that the charging profile may betailored to that particular battery. By basing a battery's chargingprocess on selected aspects of the first 104 and second 106 derivativesof the voltage response 101 curve, a charging process may be implementedthat takes into account a battery's unique and individual chargingrequirements to provide an amount of overcharge that is appropriate fora particular battery during a particular charging event.

In FIG. 1A, a voltage characteristic V(t) of an exemplary flooded deepcycle lead acid storage battery undergoing a charging cycle, controlledby a conventional ferroresonant charging process, is depicted by curve101. At the end of the charging cycle, the interrelation between thevoltage curve 101 and its first (dv/dt) 104 and second (d²v/dt²) 106derivatives can provide a useful indication of the time that at whichthe battery actually is at a certain state compared to a state of fullcharge. That certain state for a flooded lead acid battery is the stateat which the battery is at about 98% of full charge. In FIG. 1A, thatstate is identified by point 108 on the horizontal time base of thegraph.

In the voltage curve 101, the voltage increases over time until the endof the charging cycle. Prior to the end of the charging cycle, thevoltage curve begins to rise rapidly before topping out and decreasing.During the rapid increase, curve 101 has an inflection point 115 atwhich the voltage ceases to accelerate and begins to decelerate. In thecorresponding curve 104 plotting the first derivative of V(t), a maximumvalue 114 of the first derivative of V(t) occurs at the same time as theoccurrence of the inflection point 115 of V(t). The first derivative(dv/dt) of the voltage curve 101 does not again rise to a peak. Thismaximum 114 of dV/dt provides a more accurate indication of the 98%charging point 108 than does voltage inflection point 115.

The curve 104 depicting the changes in the first derivative (dv/dt), orrate of change of the voltage versus time, of a lead acid batteryundergoing ferroresonant charging, is characterized by a curve 106having two response peaks. Initially, the first derivative 104 has ahigh value corresponding to a swiftly changing battery voltage. Next thecurve 104 of rate of change of the battery voltage decreases as thevoltage curve 101 goes through a period of slight change. The smallvalues of rate of change are followed by a second rapid increase in therate of change that peaks at 114 and then falls off. The peak 114corresponds to the voltage curve 101 inflection point 115, where amaximum slope is measured. The inflection point 115 in the voltageverses time curve 101 where the voltage is changing the fastest has acorresponding maximum 114 on the first derivative curve 104. After thefirst derivative maximum has been reached, the rate of change 104 of thevoltage 101 decreases.

The second derivative (d²v/dt²) of the voltage versus time function ofthe lead acid battery undergoing ferroresonant charging is shown bycurve 106. The second derivative describes the rate of change of curve104, which in turn describes rate of voltage change. Thus, curve 106describes how the value of voltage applied to the battery terminalsaccelerates and decelerates during the battery charging process. As canbe seen from the second derivative curve 106, the second derivative iszero when the first derivative curve 104 reaches a point where its slopeis instantaneously equal to zero, such as at the previously describedmaximum 114.

The point in time at which the first derivative reaches a maximum valueand the second derivative has a value of zero very accurately identifiesthe point 108 in time when 98% of the ampere-hours previously withdrawnfrom the battery have been returned to it. The abrupt change of thesecond derivative (d²v/dt²) from a positive to a negative value iseasier to accurately identify than the gradual change in value of thefirst derivative.

Point 108 on curve 106 occurs at different times (t) for differentbatteries because this characteristic is related to the initial state ofdischarge, age and temperature characteristics of an individual battery.However, point 108 corresponds to the time in the charging process wherean impressed current 128 is nearly all being used to produce gas. Thatpoint is used as a signal in the practice of this invention, and thecharge which has been returned to the battery at that point, measuredfrom the beginning of the pertinent recharge event, is denominated asthe as the signal charge Q_(S). Knowledge of the magnitude of Q_(S) andof its relation to battery full charge Q_(F), together with the amountof overcharge Q_(o) desired, enables the total deliverable (delivered)charge Q_(D) to be determined and enables the charging process to becontrolled accordingly. If the battery is a flooded lead acid battery at80° F., Q_(S)=0.98 Q_(F). If the battery is at some other temperature,the relation of Q_(S) to Q_(F) can be different, but if the batterytemperature is not a temperature significantly below room temperature,then use of the relation Q_(S)=0.98 Q_(F) has been found to be workableand to produce significant improvements.

Charge delivered to a battery can be measured in ampere-hours(“amp-hours”). One ampere-hour is the quantity of charge delivered tothe battery in one hour by a one ampere current. Thus, a completelydrained battery having a charge capacity specified in ampere hours willtake a number of hours equal to the specified ampere-hour capacity toreturn the battery to a fully charged state to capacity, or a desiredfraction of full charge, at a one ampere charging current.

The specified amount of overcharge Q_(O) beyond full charge Q_(F) isselected to provide an increased battery life. In an exemplaryembodiment the overcharge quantity is chosen to be 108% of thereplenishment charge Q_(R). That is, in FIG. 1A, X is the time when 8%more than the replenishment charge has been delivered to the battery andis the time when the recharge event for that battery is terminated.

The amount of charge usefully returned to a battery to achieve thedesired conditioning may be found by the following relation:(specified % overcharge)(ampere-hours from start of charge to 98% offull charge)=(ampere-hours from initial charge to reach specifiedovercharge)(98%)).Stated differently using the terms defined above,Q _(S)/0.98=Q _(D)/(1+x)  (Equation 1)where x is the decimal equivalent of a percentage of the replenishmentcharge Q_(R) to be delivered to the battery as an overcharge amount. Aworkable and preferred value of x is 0.10.

Time T, point 112 in FIG. 1A, is the point in time at which the batteryis fully charged, i.e., has charge level Q_(F). Charge amount Q_(S) isfound from determining the second derivative's zero crossing. Thus, thetotal charge Q_(D) to be delivered during the recharge event may befound once Q_(S) has been found by analysis of the dynamic aspects ofthe charging characteristic curves.

The amount of overcharge to be delivered to the battery to obtain thedesired degree of conditioning by gaseous stirring of this liquidelectrolyte preferably is in the range of from about 8% to about 12%,and most preferably is about 10%.

FIGS. 1B and 1C are graphs for the charging profile of a battery at 80degrees Fahrenheit and 122 degrees Fahrenheit, respectively; while anyprofile desired can be used, the preferred profile is a constant powerprofile. In these cases, the battery delivered 135 or 136 ampere-hoursbefore the commencement of the respective recharge events. The points intime where 98% and other percentages of the charge deficiency has beenreturned to the battery are marked on each graph. A hot battery having atemperature of 122 degrees Fahrenheit reaches the 0.98 Q_(F) signalpoint earlier in time than when the second derivative of the chargingvoltage is zero valued. However, the temperature-based shift in theoccurrence of d²v/dt²=0 relative to 98% of full charge is slight. Use ofQ_(S)=0.98 Q_(F) for such a very hot battery results in far lessovercharge of the battery than would otherwise occur.

FIGS. 1D and 1E are graphs for the charging profile of a battery at 80degrees Fahrenheit and 48 degrees Fahrenheit respectively. In thesecases, the battery delivered 81 and 82 ampere-hours before commencementof the charging events. The points in time where Q_(C)=0.98 Q_(F) andQ_(C)=1.09 Q_(R) are marked on each graph. As can be seen from thosegraphs, the cold battery's signal point is shifted to the right alongthe voltage curve. For example, a cold battery will be at less than 98%of full charge at the point in time when the second derivative of thecharging voltage is zero valued. When the second voltage derivative forthe cold battery is zero valued, only 82% of the full charge has beenreturned to the battery. In such a situation, use of the relationQ_(S)=0.98 Q_(F) produces a measure of undercharge to the battery butdoes not meaningfully harm the battery. Over a typical industrialtemperature range, the percent of charge returned to a battery at thetime d²v/dt²=0 will typically vary from 84% to 102% of its total chargecapacity Q_(F.)

A straightforward way to factor temperature into a process is todirectly measure it and include it as a factor in the process. However,adding a temperature sensor which is effective to measure a battery'sinternal temperature is expensive and adds to a typical charging systemanother level of complexity that is undesirable in producing a low costcharging system that possesses an increased reliability.

FIG. 2 is a flow diagram of an exemplary charging process for a leadacid storage battery. In order to determine and utilize first and secondderivative information corresponding to the 98% charge point of abattery, a process to determine the relevant information is executed.Such a process is implemented, for example, as a program set ofinstructions that drive a computer, microprocessor or other controllingdevice that comprises a battery charging system and preferably is partof the battery charger. The instructions may be stored in volatile ornon-volatile memory or on a mass storage medium.

At the beginning of the process, a command 202 is initiated to start thecharging process. In the next step, a timer circuit is initialized 204.In an alternative process, the timer circuit can be implemented insoftware, such as would be used to direct a microprocessor to time anoperation, or sequence of operations. The time is recorded at step 206so that when the desired voltage conditions are reached, an elapsed timewill be known. Next, monitoring of the first derivative of the voltageand the second derivative of the voltage is initiated at step 208. Thevalue of the second derivative is evaluated at step 210. If the secondderivative is not equal to zero, the process continues to monitor thesecond derivative at step 208. If the second derivative is equal tozero, the process continues to the evaluation made in step 212. At step212, the first derivative of the voltage is monitored to determine if ithas reached a maximum value. If it has not, it is continued to bemonitored at step 208. If dv/dt is determined to be a maximum value atstep 212, process flow branches to step 214. At step 214, the measuredtime to reach 98% of full charge is applied and an additional chargingtime is computed so that a desired percent of overcharge may be added tothe battery. Performance of step 214 includes use of information fromthe timer and information about total amperes delivered to the batteryto compute Q_(S), and to compute Q_(D) using the relations describedabove and program parameters defining the desired value of x (percentageovercharge) and Q_(S)/Q_(F).

In an embodiment of the invention, the evaluations performed at steps210 and 212 may be interchanged without affecting the outcome of theprocess. Additionally, determination of the maximum of the firstderivative of the voltage performed in exemplary step 212 may be donecontinuously or by utilizing sampling methods known to those skilled inthe art.

After the initial charging time, from initiation of the charging cycleuntil d²v/dt²=0, has been determined and the additional amount of timeto provide a desired overcharge is calculated at step 214, the process(step 216) directs the battery to be charged for an additional amount oftime to provide the desired overcharge. After the additional chargingtime has elapsed, the charging cycle is stopped at step 218.

A relation which is useful to determine when a battery rechargingprocess according to this invention is to be terminated is as follows:Q _(S)/0.98=Q _(D)/(1+x)in which Q_(S) and Q_(D) are as defined above (see Glossary), and x isthe decimal equivalent of the percentage of the replenishment chargeQ_(R) to be applied to the battery, after it is fully charged, toachieve the desired conditioning (electrolyte stirring) of the battery.

It is apparent that the difference between Q_(D) and Q_(S) is thequantity of charging energy which remains to be delivered to the batteryin the course of the battery recharging event between the time the pointof 98% of full charge of the battery is detected and the time at whichthe recharge event is ended. Thus, the quantity of charging energy to bedelivered to the battery after charging energy amount Q_(S) has beendelivered can be determined by evaluation of the following expression:Q _(S){[1+x)/0.98]−1}.This is true because Q_(D=Q) _(S)(1+x)/0.98.

Assume that the full charge of a battery is 1000, and the desiredovercharge percentage is 8%. If a battery is 50% discharged at thebeginning of a recharge event, Q_(S)=0.98 (1000−500)=490, and soQ_(D)=540. Q_(i)+Q_(D)=500+540=1040, and so the actual amount ofovercharge at termination of the recharge event is 40.

Applying the same assumptions to a battery which is at 25% capacity(Q_(i)=250) when recharging begins, Q_(S)=0.98 (1000−250)=735,Q_(D)=810, Q_(i)+Q_(D)=250+810=1060, and so the delivered overcharge is60. Similarly, if the battery is at 70% of capacity when rechargingbegins, Q_(S)=0.98 (1000−700)=294, Q_(D)=324, Q_(i)+Q_(D)=700+324=1024,and so the delivered overcharge is 24.

It will be recalled that if a battery is very deeply discharged when itsrecharging event begins, the specific gravity of the acid electrolyte islow (near 1.00) due to the highly diluted state of the electrolyte. Themore dilute the electrolyte when recharging begins, the greater will bethe density stratification of the electrolyte at full charge, and so themore the electrolyte needs to be stirred by gas generation to properlycondition the battery by making the electrolyte substantially homogenousthrough the battery cells. Conversely, if a battery is relativelylightly discharged when its recharging event begins, the acidelectrolyte will have a higher starting specific gravity, a lowerdensity stratification at full charge, and a lower need for electrolytestirring to properly condition the battery. The foregoing examples showthat this invention delivers to a recharged battery only that amount ofovercharge which is determined to be needed for proper conditioning anddoes not excessively overcharge the battery. The amount by which thebattery is overcharged is a function of the discharge state of thebattery when recharging begins. The point at which the rechargingprocess is ended is determined from information obtained from thebattery itself. That is a characteristic of the battery rechargeprocesses illustrated in FIGS. 2–7.

FIGS. 3A and 3B are flow diagrams of a charging process that monitorscell voltage. Steps 302–316 can be the same as steps 202–216. However,in this process charging is not terminated unless certain minimumconditions are satisfied. In the exemplary embodiment, cell voltage isone such minimum condition. At step 318, the cell voltage is monitored.If the cell voltages have reached, say, 2.45 volts per cell, thecharging algorithm is terminated at step 320. Alternatively other cellvoltages may be utilized for other types of batteries.

If the cell voltage has not reached 2.45 volts per cell, the processbranches to letter A in FIG. 3B. In this process, charging defaults to astate that does not terminate the charging process until the firstderivative voltage equals zero. Thus, charging continues at step 322.While charging, the first derivative continues to be evaluated at step324. If the first derivative reaches zero, the charging process is thenended at step 326. If the first derivative does not reach zero, thecharging process continues until the first derivative reaches zero andthe process is ended.

FIGS. 4A and 4B are a flow diagram of a charging process that monitorscell voltage and charging time to produce a desired overcharge. Thisprocess is an alternative embodiment of the process of FIG. 3. Theprocess shown in FIG. 4A is analogous to the process of FIG. 3A, andsteps 402–426 can be the same as steps 302–326. However, in thisprocess, charging is not terminated unless certain minimum conditionsare satisfied. Cell voltage can be one such minimum condition. At step418, the cell voltage is monitored.

The process shown in FIGS. 4A and 4B provides a further back-up ofterminating the charging cycle if charging has not been accomplished ina certain number of hours, as may be deemed desirable in a particularapplication. In the embodiment described, 16 hours is deemed the maximumnumber of hours to accomplish a full charge. Alternatively, any timeperiod suitable to prevent damage to a battery may be substituted.

Continuing with FIG. 4B, the charging process continues in step 422while the first voltage derivative is monitored at step 424. If thefirst derivative reaches zero, the charging process is ended at step426. If the first voltage derivative has not reached zero, the processbranches to an evaluation step 428 that compares the elapsed chargingtime to a set time, in this case 16 hours. In an embodiment any suitabletime period may be selected as the set time.

If the predetermined charging time has been exceeded, an alarm signal ormessage may be sent (step 430) visibly, audibly or otherwise to theperson in charge of or overseeing the battery recharging process. Themessage can include information on the identity of the charger ofinterest, to distinguish it from other chargers which may be present, aswhen batteries in each of the golf cars in a fleet are being rechargedat the same time. Upon activation of the alarm signal by step 430, thecharging cycle is terminated at step 432. If at step 428 thepredetermined time has not been exceeded, the charging cycle continues.

FIG. 5 is a flow diagram of a charging process that provides refreshcharging. Steps 502–516 can be the same as steps 402–416. The chargingprocess can be terminated at step 518.

While the battery is still connected to the charger, the open circuitvoltage of the battery is monitored at step 520. If the battery'svoltage falls below a preset minimum value V_(Min), the charging processis caused to be repeated. The voltage V_(Min) is selected to provide adesired lower threshold of voltage that the charger will not allow thebattery to drop below. The charger keeps a charge on the battery to keepit above V_(Min). However, as long as the battery remains above the lowvoltage threshold V_(Min), the charging process will not be reinitiated,and the overall process is stopped at step 522. The value selected forV_(Min) is based upon an amount of acceptable remaining charge that isuser selectable, or alternatively programable as a preset value in thecharges operating program.

FIG. 6 is a flow diagram of a charging process that monitors an elapsedtime since termination of charging of a battery, and the battery opencircuit voltage. Steps 602–618 can be the same as steps 502–518. In thischarging process which monitors an elapsed time since termination ofcharging of a battery, and the battery open circuit voltage, the timeelapsed since termination of the charging process is monitored at step622. If a predetermined amount of time has elapsed since the chargingprocess was terminated and the battery continues to be connected to thecharger equipment, then the charging process is reinitiated. If theelapsed time has not exceeded the predetermined amount of time theprocess proceeds to step 624. If the open circuit voltage is less thanits predetermined value V_(Min) then charging is reinitiated. If thebattery open circuit voltage remains above V_(Min) then the process isterminated at step 626.

In an alternative process, the open circuit voltage can be monitoredprior to evaluating time since termination of the charging process. In afurther alternative process, time since termination of the chargingprocess can be monitored simultaneously with monitoring of the batteryopen circuit voltage.

FIG. 7 is a flow diagram of a form of the invention that allows theselection of various charging profiles. At step 702 the charging processis initiated. Next, a charging profile is selected 704. Possiblecharging profiles comprise: constant potential; modified constantpotential; constant current; ferro and ferro resonant; constantcurrent-constant potential-constant current IEI); constantpower-constant potential-constant current (PEI); and, preferably,constant power. Information describing and defining the differentprofiles can be contained in an addressable memory included in thecharger in association with the control aspects of the charger.

Once a charging profile has been selected, a timer circuit is initialedand the process is at step 706 started utilizing the selected profile.Next, the process begins recording an elapsed time at step 708. Theprocess monitors the first and second derivatives of the voltage at step710. If the second derivative is equal to zero (step 712) and the firstderivative has reached a maximum (step 714), the charging processcontinues. If the second derivative has not reached zero and the firstderivative has not reached the maximum, their values are continuouslymonitored until they reach the desired values.

Once the desired derivative values have been reached, an additionalcharging time for a desired overcharge is calculated at step 716, andthe battery is charged for an additional charging time for the desiredovercharge (step 718). The additional charging time may utilize thepreviously selected charging profile or another charging profile. Oncethe additional charging time for the desired overcharge has elapsed, theprocess is terminated at step 720.

FIG. 8 is a block diagram of an exemplary battery charging systemutilizing a charge control algorithm device IC and a “measuringcomputing and control device” (MCCD) such as a suitably programmedmicroprocessor. An AC input 802 to rectifier 804 creates a chargingcurrent, at a desired voltage, that is applied to battery 810 through acharge process control device integrated circuit 808. The charge processcontrol device integrated circuit 808 controls application of thecharging energy to the battery 810.

The charge control device IC 808 functions in conjunction with the MCCDto apply a charging signal comprising one or more charging profiles orprocesses. Instructions to implement one or more of the processesdescribed in FIGS. 2 through 7 can be stored in the MCCD 806. Typicallystorage is achieved by loading a set of program instructions describingthe process into the MCCD. Alternatively, the process may be integratedinto a custom charge process control integrated circuit which mayinclude the features and functions of integrated circuit 808.

FIG. 9 is a block diagram of a battery charging system capable ofimplementing one or more of the invention's charging processes to chargea battery. An AC input 902 is controlled by relay 912. The AC power isapplied to rectifier 904 to produce a DC voltage having a ripplecomponent. Voltage regulator 906 reduces the variations in the DCvoltage. The regulated DC voltage is applied to a conventionallyconstructed series pass element 908 that works in conjunction with aconventionally constructed current limiting device 910 to supply adesired current and voltage through the contacts of a relay 914 tobattery 916. Current applied to the battery is monitored by aconventional ampere meter 918. The ampere meter monitors theinstantaneous value of current flowing in a conductor. In an alternativearrangement, a conventional averaging ampere meter can be used toindicate an average charge passing through the conductor. In a furtheralternative arrangement a conventional totalizing ampere meter can beused to provide an indication of the total charge passing through theconductor. Voltage across the battery terminals is monitored by voltmeter 920. Information obtained from the ampere meter and the volt metercan be supplied to MCCD 806.

The voltage across the battery 916 is also supplied to a differentiatorcircuit 922 that computes the first derivative of the voltage. Such acircuit may be conventionally constructed as shown at 930. Adifferentiator typically comprises an operational amplifier A, aresistor R and a capacitor C, connected as known by those skilled intothe art to produce a differentiator. A voltage V_(i) is applied to theinput of the differentiator. The signal output V_(o) is equal to−RC(dV/dt).

The output of the first derivative circuit 922 is fed into a peakdetector 928. When a maximum first derivative signal is detected, anindication is provided to MCCD 806. The output of the first derivativeprocessing circuit is also fed to a second derivative processing circuit924. This circuit is simply a replica of the circuit in 922. The outputof the second derivative circuit 924 is fed to a zero crossing detector926. A zero crossing detector is a circuit that detects a transition insignal polarity, such as when a voltage goes from positive to negativeand by necessity crosses through a value of zero volts. Detection of azero crossing corresponding to the detection of inflection point 115 involtage curve 101 of FIG. 1 is sought. An indication of the detection ofa zero crossing is provided to the MCCD 806. Under control of theprocess comprising an embodiment of the invention, the MCCD directs acharging current and voltage to be applied through relay 914. The MCCDalso can control the operation of the AC input through relay 912.

It is preferred that the components of the charging system depicted inFIG. 9 be housed in a common charger housing. The charger can be,usually is, separate from the battery or thing (e.g., golf car) in whichthe battery is located. However, if desired, some or all of thecomponents of the charging system can be physically associated with thebattery as elements of, e.g., a golf car.

It will be seen that this invention provides equipment and proceduresfor charging a flooded lead acid battery of the deep cycle type in wayswhich charge the battery effectively yet without overly charging thebattery to extents which reduce battery life. The battery is overchargedby an amount which is a selected percentage of the charging energyrequired to place the battery in a state of full charge followingcompletion of its last preceding duty cycle. A recharging event achievedin the practice of this invention inherently allows for and takes intoconsideration factors such as the battery, age and internalcharacteristics which impact charging effectiveness and efficiency.

While the invention has been described above with reference torecharging a battery, it will be understood that the invention alsoapplies to the recharging of a set of batteries which may be encounteredin an electric golf car or some other electrically powered vehicle ordevice, or with a set of batteries used in connection with aphotovoltaic electrical power system, for example.

The foregoing description of preferred and other embodiments and formsof the invention has been presented by way of example, not as a catalogof all forms which equipment or procedures in which the invention can bemanifested or used to advantage. Workers skilled in the art to which theinvention pertains will understand that variations and modifications ofthe described equipment and processes can be used beneficially withoutdeparting from the scope of the invention.

1. A method for charging flooded deep cycle lead acid batteriescomprising the steps of: applying charging energy to such a battery;monitoring the charging energy as to quantity delivered to the batteryand its dv/dt and d²v/dt² aspects; by use of information about a firstamount of charging energy delivered to the battery to a point in theprocess when dv/dt is a maximum and d²v/dt²=0, determining at that pointand delivering to the battery beyond that point a defined quantity ofcharging energy additive to said first amount adequate to overcharge thebattery to a predetermined extent related to said first amount.
 2. Amethod for charging flooded deep cycle lead acid batteries comprisingthe steps of: applying to such a battery a first amount of chargingenergy adequate, in combination with an initial charge condition of thebattery, to cause the battery to attain a detectable charge state whichis less than a full charge condition and which has a known relation to afull charge condition, and applying to the battery a further secondincrement of charging energy which is adequate, in combination with theinitial charge condition and the first amount of charging energy, toovercharge the battery to a selected extent and the quantity of which isdetermined as a selected percentage of the first amount of chargingenergy when the detectable charge state is attained.
 3. The method asclaimed in claim 2 in which the detectable charge state is the state atwhich the battery is at substantially 98% of full charge.
 4. The methodas claimed in claim 3 in which the step of determining the amount of thefurther second increment of charging energy includes: dividing a) theproduct of (i) first amount of charging energy and (ii) the sum of unity(one) and the decimal equivalent of the percent of overcharge by b)0.98.
 5. The method as claimed in claim 4 in which the step ofdetermining the amount of the second increment of charging energyfurther includes determining the difference between a) the result of thedivision operation described in claim 4 and b) the first amount ofcharging energy.
 6. The method as claimed in claim 2 in which thedetectable charge state is detected by: determining when the rate ofchange of an applied charging voltage with respect to time (dv/dt) is amaximum; and determining when the acceleration of the applied chargingvoltage with respect to time (d²v/dt²) is zero.
 7. A method for chargingdeep cycle lead acid batteries comprising: applying charging energy tosuch a battery; detecting a point of 98% of full charge in the chargingprocess; monitoring the charging energy provided in amp hours to attainthe 98% full charge point; determining the remaining charging energy tobe applied to fully charge the battery and to overcharge the battery byan amount substantially equal to a predetermined percentage of thequantity of energy applied to the battery from the commencement ofcharging to the 98% full charge point of the battery; and applying theremaining charging energy to the battery.
 8. The method of claim 7 forcharging a deep cycle lead acid battery wherein the step of detectingthe 98% full charge point comprises: determining when the rate of changeof an applied charging voltage with respect to time (dv/dt) is amaximum; and determining when the acceleration of the applied chargingvoltage with respect to time (d²v/dt²) is zero.
 9. Apparatus forcharging flooded deep cycle lead acid batteries which includes a DCsource, a mechanism operable to measure the amount of charging energydelivered to a battery from the beginning of a battery charging event,and a mechanism operative for detecting when a battery being charged bythe apparatus is at a detectable point in a charging event at which thebattery has a certain state of charge less than full charge and fordetermining at that point and controlling the application to the batterybeyond that point of a further quantity of charging energy effective toovercharge the battery by a selected percentage of the amount ofcharging energy delivered to the battery to that detectable point inthat charging event.
 10. Apparatus as claimed in claim 9 furtherincluding: a dv/dt measurement circuit, a d²v/dt² measurement circuit,and a controller coupled to the dv/dt and d²v/dt² measurement circuits,the controller being configured for detecting the point in a batteryrecharge event at which dv/dt is a maximum and d²v/dt²=0, and at whichthe battery is at substantially a certain percentage of full charge, andfor determining the value of Q_(D) from the relation Q_(S)/p=Q_(D)/(1+x) in which Q_(S) is the ampere-hours of charging energydelivered to the battery in the interval from the beginning of therecharge event to the detected point, p is the decimal equivalent of thecertain percentage, x is the decimal equivalent of a desired percentageamount of replenishment charge to be delivered to the battery as anovercharge amount, and Q_(D) is the total amount of charging energy tobe delivered to the battery from the beginning of the recharge event tothe end of that event.
 11. Apparatus according to claim 10 in which thevalue of p is substantially 0.98.
 12. Apparatus according to claim 10 inwhich x is in the range of from about 0.08 to about 0.12.